Problem: Simplify the following expression: $x = \dfrac{-30q - 9}{-24q + 15}$ You can assume $q \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-30q - 9 = - (2\cdot3\cdot5 \cdot q) - (3\cdot3)$ The denominator can be factored: $-24q + 15 = - (2\cdot2\cdot2\cdot3 \cdot q) + (3\cdot5)$ The greatest common factor of all the terms is $3$ Factoring out $3$ gives us: $x = \dfrac{(3)(-10q - 3)}{(3)(-8q + 5)}$ Dividing both the numerator and denominator by $3$ gives: $x = \dfrac{-10q - 3}{-8q + 5}$